I have the following problem. I need to find the volume of the shape that is bounded up by $$u(x,y)=13+x^2$$ and down by $$v(x,y)=7x+4y$$ and from its sides by the cylinder $$x^2+y^2=1.$$ Now I know I need to do to the integral $\displaystyle \iint\limits_D \left(u(x,y)-v(x,y) \right)dxdy$
But I dont really know how to define $D$, I know that is by the projection in $XY$ plane.
I tried to draw it in the $XY$ plane, drew the cylinder and the plane $z=7x+4y$. But I don't really know where to go next.
Some tips will really help me! :)